The pot with the roots hanging out and drooping plant. It needs to be potted up. When watering any plant always water it well and let it drain. I am not fond of the 1 cup method. It does not necessarily wet all the soil and dry spots can be hard to re wet. Not watering to flush the pot can also build up salts which only a few plants can tolerate. Lavenders grow best in zones 5-8. Lavender multifida (species) grows and blooms nearly all year in zones 8-10. Lavandins are a cross between lavendula x intermedia. They are sterile hybrids but are more adaptable in warmer zones.
Lavender likes sun and does not like water on its leaves for any length of time or they leaves will turn black.
In the examples above, the pots were chosen more for aesthetics than function. A porous pot dries better. Unglazed terra cotta or cement breathes better. The soil mixes also look really organic, but organic mixes hold water more. I would use a cactus mix or basically one part perlite, one part peat moss. Since lavender does like alkaline conditions more, a little bit of dolomite lime (1/2 teaspoon mixed in the soil does not hurt).
Watering should always be as needed and not on a schedule. The type of pot, potting mix, location, air circulation, if you have a saucer (no saucer is best or at least use pot feet and keep the bottom out of the saucer). Once every 11 days is too long even for a potted plant. If the soil is not drying out in 3 days, the mix needs to be drier, or the pot smaller or both., and the plant needs more air circulation. Lavender has a high light requirement and should be hardened off to an outside location whenever the weather is good.
Lavender does not need a lot of fertilizer so I only use osmocote in pots. I keep most of the lavender in pots because it can rain for weeks in the rainy season and I need to be able to move the pots under the eaves where they will stay drier. In the ground, lavender can be a large mounding shrub three feet high and wide. It does need to be pruned annually to keep it from getting woody. Only green wood should be pruned. I usually prune half the plant and wait for the new shoots to sprout before I prune off the other half. I lose fewer plants that way. My front yard slopes. it is good for lavender to be where it never puddles. I have to work on making sure it isn't where the rain drops off the roof either.
Lavender does not go dormant in my climate so, I don't know about winter care. I grow mostly Provence, MultifIda, Dentata, Otto Quast, stoechas, Fred Boutin, Grosso, and other lavendins which are more adapted to zone 11. L. MultifIda blooms almost all year. The others bloom for a few weeks in summer. Zone 5 lavenders like munstead, hidcote, and lavender lady are more like annuals here.
https://purplehazelavender.com/lavender ... -lavender/
https://www.gardenia.net/guide/planting ... er-in-pots
Happy gardening in Hawaii. Gardens are where people grow.